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A Detailed Look ...

... at spatial interpolation, temporal integration, and input/output

    1. put together uvetc dictionnary
    • read gridded velocity output (Udata, Vdata)
    • read trajectory output (float_traj*data)
    1. interpolate U,V along trajectory from gridded output
    • compare with u,v from float_traj*data
    1. compute whole trajectory using OrdinaryDiffEq.jl
    • compare with x(t),y(t) from float_traj*data

Notes: For additional documentation see e.g. 1, 2, 3, 4

1. import software

using IndividualDisplacements, OrdinaryDiffEq
p=dirname(pathof(IndividualDisplacements))
include(joinpath(p,"../examples/recipes_plots.jl"))
include(joinpath(p,"../examples/example123.jl"))
include(joinpath(p,"../examples/helper_functions.jl"))
Main.ex-detailed_look.setup_random_flow

2. reload trajectories from MITgcm/pkg/flt

get_flt_ex_if_needed()
dirIn=joinpath(p,"../examples/flt_example/")
prec=Float32
df=read_flt(dirIn,prec) #function exported by IndividualDisplacements
plt=PlotBasic(df,300,100000.0)
0 1×10 5 2×10 5 3×10 5 4×10 5 0 5.0×10 4 1.0×10 5 1.5×10 5 2.0×10 5

3. Read gridded variables via MeshArrays.jl

Put gridded variables in a dictionary.

uvetc=example2_setup()
Dict{String,Any} with 13 entries:
  "t0"   => 0.0
  "YC"   =>   data type   = Float32…
  "v1"   =>   data type   = Float64…
  "mskW" =>   data type   = Float64…
  "dx"   => 5000.0
  "u1"   =>   data type   = Float64…
  "XG"   =>   data type   = Float32…
  "YG"   =>   data type   = Float32…
  "u0"   =>   data type   = Float64…
  "mskS" =>   data type   = Float64…
  "t1"   => 6.48036e7
  "XC"   =>   data type   = Float32…
  "v0"   =>   data type   = Float64…

4. Visualize velocity fields

plt=heatmap(uvetc["mskW"][1,1].*uvetc["u0"][1,1],title="U at the start")
display(plt)

plt=heatmap(uvetc["mskW"][1,1].*uvetc["u1"][1,1]-uvetc["u0"][1,1],title="U end - U start")
display(plt)
/home/travis/.julia/packages/GR/yMV3y/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine DRAW_IMAGE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine CELLARRAY
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine DRAW_IMAGE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine CELLARRAY
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT

5. Visualize trajectories from MITgcm/pkg/flt

Select one trajectory

tmp=df[df.ID .== 200, :]
tmp[1:4,:]

4 rows × 14 columns

IDtimelonlatdepijketaNuVelvVelthetasalttile
Int64Int64Float32Float32Float32Float32Float32Float32Float32Float32Float32Float32Float32Int64
12003600187630.021119.0-1406.2538.0264.723793.00.114312-0.03859630.01014730.29864335.01
220072001.87491e521155.8-1406.2537.99824.731153.00.114318-0.03871940.01028620.29864335.01
3200108001.87351e521193.1-1406.2537.97024.738613.00.114313-0.03884170.0104430.29864335.01
4200144001.87211e521230.9-1406.2537.94224.746193.00.11431-0.03896310.01059940.29864335.01

Super-impose trajectory over velocity field (first for u ...)

x=uvetc["XG"].f[1][:,1]
y=uvetc["YC"].f[1][1,:]
z=transpose(uvetc["mskW"][1].*uvetc["u0"][1,1])
plt=contourf(x,y,z,c=:delta)
plot!(tmp[:,:lon],tmp[:,:lat],c=:red,w=4,leg=false)
0 1×10 5 2×10 5 3×10 5 4×10 5 0 5.0×10 4 1.0×10 5 1.5×10 5 2.0×10 5 - 0.00003 - 0.00002 - 0.00001 0 0.00001 0.00002 0.00003

Super-impose trajectory over velocity field (... then for v)

x=uvetc["XC"].f[1][:,1]
y=uvetc["YG"].f[1][1,:]
z=transpose(uvetc["mskW"][1].*uvetc["v0"][1,1])
plt=contourf(x,y,z,c=:delta)
plot!(tmp[:,:lon],tmp[:,:lat],c=:red,w=4,leg=false)
0 1×10 5 2×10 5 3×10 5 4×10 5 0 5.0×10 4 1.0×10 5 1.5×10 5 2.0×10 5 - 0.00005 - 0.000025 0 0.000025 0.00005

6. Recompute displacements from gridded flow fields

uInit=[tmp[1,:lon];tmp[1,:lat]]./uvetc["dx"]
nSteps=Int32(tmp[end,:time]/3600)-2
du=fill(0.0,2);

Visualize and compare with actual grid point values – jumps on the tangential component are expected with linear scheme:

tmpu=fill(0.0,100)
tmpv=fill(0.0,100)
tmpx=fill(0.0,100)
for i=1:100
    tmpx[i]=500.0 *i./uvetc["dx"]
    ⬡(du,[tmpx[i];0.499./uvetc["dx"]],uvetc,0.0)
    tmpu[i]=du[1]
    tmpv[i]=du[2]
end
plt=plot(tmpx,tmpu,label="u (interp)")
plot!(uvetc["XG"].f[1][1:10,1]./uvetc["dx"],uvetc["u0"].f[1][1:10,1],marker=:o,label="u (C-grid)")
plot!(tmpx,tmpv,label="v (interp)")
plot!(uvetc["XG"].f[1][1:10,1]./uvetc["dx"],uvetc["v0"].f[1][1:10,1],marker=:o,label="v (C-grid)")
display(plt)

tmpu=fill(0.0,100)
tmpv=fill(0.0,100)
tmpy=fill(0.0,100)
for i=1:100
    tmpy[i]=500.0 *i./uvetc["dx"]
    ⬡(du,[0.499./uvetc["dx"];tmpy[i]],uvetc,0.0)
    tmpu[i]=du[1]
    tmpv[i]=du[2]
end
plt=plot(tmpx,tmpu,label="u (interp)")
plot!(uvetc["YG"].f[1][1,1:10]./uvetc["dx"],uvetc["u0"].f[1][1,1:10],marker=:o,label="u (C-grid)")
plot!(tmpx,tmpv,label="v (interp)")
plot!(uvetc["YG"].f[1][1,1:10]./uvetc["dx"],uvetc["v0"].f[1][1,1:10],marker=:o,label="v (C-grid)")
display(plt)
/home/travis/.julia/packages/GR/yMV3y/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYMARKER

Compare recomputed velocities with those from pkg/flt

nSteps=2998
tmpu=fill(0.0,nSteps); tmpv=fill(0.0,nSteps);
tmpx=fill(0.0,nSteps); tmpy=fill(0.0,nSteps);
refu=fill(0.0,nSteps); refv=fill(0.0,nSteps);
for i=1:nSteps
    □(du,[tmp[i,:lon],tmp[i,:lat]],tmp,tmp[i,:time])
    refu[i]=du[1]./uvetc["dx"]
    refv[i]=du[2]./uvetc["dx"]
    ⬡(du,[tmp[i,:lon],tmp[i,:lat]]./uvetc["dx"],uvetc,tmp[i,:time])
    tmpu[i]=du[1]
    tmpv[i]=du[2]
end
plt=plot(tmpu,label="u")
plot!(tmpv,label="v")
plot!(refu,label="u (ref)")
plot!(refv,label="v (ref)")
display(plt)
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE

6. Recompute trajectories from gridded flow fields

Solve through time using OrdinaryDiffEq.jl with

  • ⬡ is the function computing du/dt
  • uInit is the initial condition u @ tspan[1]
  • tspan is the time interval
  • uvetc are parameters for ⬡
  • Tsit5 is the time-stepping scheme
  • reltol and abstol are tolerance parameters
tspan = (0.0,nSteps*3600.0)
#prob = ODEProblem(□,uInit,tspan,tmp)
prob = ODEProblem(⬡,uInit,tspan,uvetc)
sol = solve(prob,Tsit5(),reltol=1e-8,abstol=1e-8)
sol[1:4]
retcode: Success
Interpolation: specialized 4th order "free" interpolation
t: 4-element Array{Float64,1}:
  0.0               
  0.2007818920948153
  2.2086008130429686
 22.2867900225245   
u: 4-element Array{Array{Float64,1},1}:
 [37.525990625, 4.22379453125]         
 [37.52598925375626, 4.223794946058778]
 [37.52597554129228, 4.223799094139329]
 [37.5258384139952, 4.223840574222589]

Compare recomputed trajectories with those from pkg/flt

ref=transpose([tmp[1:nSteps,:lon] tmp[1:nSteps,:lat]])
maxLon=80*5.e3
maxLat=42*5.e3
show(size(ref))
for i=1:nSteps-1
    ref[1,i+1]-ref[1,i]>maxLon/2 ? ref[1,i+1:end]-=fill(maxLon,(nSteps-i)) : nothing
    ref[1,i+1]-ref[1,i]<-maxLon/2 ? ref[1,i+1:end]+=fill(maxLon,(nSteps-i)) : nothing
    ref[2,i+1]-ref[2,i]>maxLat/2 ? ref[2,i+1:end]-=fill(maxLat,(nSteps-i)) : nothing
    ref[2,i+1]-ref[2,i]<-maxLat/2 ? ref[2,i+1:end]+=fill(maxLat,(nSteps-i)) : nothing
end
ref=ref./uvetc["dx"]

plt=plot(sol[1,:],sol[2,:],linewidth=5,title="Using Recomputed Velocities",
     xaxis="lon",yaxis="lat",label="Julia Solution") # legend=false
plot!(ref[1,:],ref[2,:],lw=3,ls=:dash,label="MITgcm Solution")
display(plt)
(2, 2998)GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine FILLAREA
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine TEXT
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE
GKS: GKS not in proper state. GKS must be either in the state WSAC or SGOP in routine POLYLINE

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